It's quite normal. In a fandom, people are interested in different aspects of the characters. Zane might be curious about Syrus's backstory, relationships, or potential storylines that fanfiction writers have created. It's just another way of engaging with the fictional world they are part of.
Perhaps Zane is a big fan of Syrus himself and by reading the fanfiction, he gets to delve deeper into the Syrus - centric stories. It could also be that he enjoys the creativity of the fanfiction community and how they expand on the Syrus character in ways the original work might not have.
It could mean that Zane is interested in Syrus's story as told in the fan - created fictional works. Maybe he wants to understand Syrus better through the different interpretations in the fanfiction.
Another aspect of their brotherly love in fanfiction could be the way they support each other during tough times. Syrus might be having a hard time with his self - confidence, and Zane would be there to encourage him. He could tell Syrus about his own insecurities when he was younger and how he overcame them, thus inspiring Syrus to grow and believe in himself more.
There's no way to really say if it's common without knowing more about Zane. If he has a lot of free time and is a die - hard fan of the source material involving Syrus, then it might be a regular pastime for him. However, if he's not that into the whole fan culture or Syrus specifically, it would be less common.
At first, their relationship might become strained. Zane's anger could make Syrus confused and a bit scared. Syrus might try to avoid Zane, not knowing how to deal with his anger.
One possible reason could be jealousy. Maybe Syrus is getting more attention in the fanfiction world, and Zane, being a proud character, doesn't like that. For example, if Syrus is praised for his skills while Zane feels overlooked, it can make him mad.
The growth of their brotherly love can also be a theme. As Syrus matures, he starts to understand Zane better. He realizes that Zane's strictness was always out of love and a desire for him to become a better person. In turn, Zane sees Syrus growing into a confident individual, and this makes him proud and further strengthens their brotherly connection.